Calculate the rate of energy loss by electron due to inverse Compton scattering by assuming the energy density of the photon with which the electrons are colliding 8.6 xx 10° J/m', speed parameter as 0.14, and Lorentz factor as 19.8

aftredingzo

aftredingzo

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2022-08-20

Calculate the rate of energy loss by electron due to inverse Compton scattering by assuming the energy density of the photon with which the electrons are colliding 8.6 × 10   J / m , speed parameter as 0.14, and Lorentz factor as 19.8.

Answer & Explanation

Katrina Fisher

Katrina Fisher

Beginner2022-08-21Added 3 answers

Given an electron undergoing an inverse Compton scattering.
Given the parameters,
Energy density
u rad = 8.6 × 10 6   J / m 3
Speed parameter
β = 0.14
Lorentz Factor
γ = 19.8
The energy loss rate in the Inverse Compton Effect is given by
d E d t = 4 3 σ T c u rad β 2 γ 2
Where
σ T = 6.65 × 10 29 m 2
is the Thompson's Cross−section, and
c = 3 × 10 8   m / s
Substituting the values
d E d t = 4 3 × 6.65 × 10 29 × 3 × 10 8 × 10 6 × ( 0.14 ) 2 × ( 19.8 ) 2 d E d t = 228.76 × 10 27 × 0.0196 × 392.04 d E d t = 1 , 757.79 × 10 27   W d E d t 1.75 × 10 24   W

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